In addition to studying the energy spectra we also analyze the wavefunctions for the resulting isolated narrow bands. First, we do so by computing the sublattice polarization as well as the Wilson loops [1]}, [2]}, [3]}.
Second, we quantify the degree of the p-h asymmetry in our continuum models for different momenta in the moire BZ by computing the deviation from unitarity of the momentum resolved projected p-h operator. Momentum averaged version of this operator was analyzed for the BM model in Ref. [4]}, where p-h symmetry was found to be nearly perfect. We define the deviation from unitarity as the difference of the smallest singular value from unity, confirming the finding of Ref. [4]} of nearly perfect p-h symmetry in the BM model where the p-h is broken by at most \(1\%\)  near the \(\Gamma \) 
point. Further, we do this analysis for the continuum model obtained from the tight binding model of Ref. [6]}, with relaxed lattice configuration, where we find at most \(1.8\%\)  deviation from unitarity near the \(\Gamma \)  point (see Fig. REF ). On the other hand, for the continuum model obtained from the tight binding model of the Ref. [7]}, interestingly, the p-h symmetry is broken by \(\sim 16\%\)  near the \(\Gamma \)  point (see Fig. REF ). The stronger p-h symmetry breaking in the model of Ref. [7]} is due to the angle dependence of the microscopic inter-layer hopping, resulting in a larger p-h symmetry breaking contact inter-layer tunneling term in the continuum theory, which we dubbed \(w_3\)  previously (see the supplementary material of Ref. [9]}).
The significance of such sizable p-h symmetry breaking for the correlated states will be presented in a separate paper.
